Aircraft toilets always sound pretty damn loud to me. And their main reason to exist on planes is the lack of available water. Pretty sure that is not an aircraft carrier’s constraint.
EDIT: See https://www.navy.mil/submit/display.asp?story_id=103122 for a 2017 press release describing how the Reactor Department produces fresh water aboard the aircraft carrier USS Abraham Lincoln (a Nimitz-class carrier, i.e., an old design). TL;DR: It's done with giant evaporators, that is, distilling units.
Fun fact: At sea, one of the big uses of fresh water aboard a carrier is the repeated washing down of the aircraft to reduce corrosion from the salt air.